The Seven Crystal
Systems
Prof. Dr. Ziad Abu-Hamatteh
Faculty of Engineering Technology
Al-Balqa’ Applied University
The seven crystal systems are a method of
classifying crystals according to their atomic lattice
or structure. The structures of all crystals can be
classified according to the symmetry of the unit cells.
There are in total 7 groups, collectively called Crystal
Systems: Triclinic, Monoclinic, Orthorhombic,
Tetragonal, Trigonal, Hexagonal, and Cubic. The
symmetry of each group is described by the
relationship between the lattice sides a, b, and c and
angles α, β and γ.
Cubic System
The Cubic crystal system has the highest
symmetry. It also has the greatest number of
restrictions. Not only do all the angles equal
90°, but all the sides have the same length as
well.
a = b = c
α = β = γ = 90°
Common Cubic Crystals: Diamond,
Fluorite, Garnet, Pyrite
Hexagonal System
The Hexagonal crystal system can be
visualized as a prism with hexagons as the
bases. In order to describe it in terms of a, b, c
and the three angles, we introduce restrictions
such as γ must equal 120°.
a = b ≠c [a1=a2=a3 ≠c]
α = β = 90° and γ = 120°
Common Hexagonal Crystals: Apatite, Beryl,
Emerald
Trigonal System
For the Trigonal, also known as
Rhombohedral, crystal system, the length of
the sides and the angles are equal, but the
shape of the cell is harder to visualize.
a = b = c
α = β = γ ≠90°
Common Trigonal Crystals: Agate, Calcite,
Hematite, Jasper, Quartz, Sapphire, Smoky
Quartz, Tigers Eye, Tourmaline
Tetragonal System
In the Tetragonal crystal system we introduce
yet another restriction. Now, not only do all
the angles have to equal 90°, but the two sides
a and b have to be the same length too. This
makes the c side a symmetry unique axis.
a = b ≠c
α = β = γ = 90°
Common Tetragonal Crystals: Zircon
Orthorhombic System
In the Orthorhombic crystal system, all the
angles must be 90°. The sides, on the other
hand, can change independently of each other.
a ≠b ≠c
α = β = γ = 90°
Common Orthorhombic Crystals: Topaz, Zoisite
Monoclinic System
Monoclinic crystal system introduces a
restriction on two of the angles. Now α and γ
must equal to 90°. This makes the b side the
symmetry unique axis.
a ≠b ≠c
α = γ = 90° and β ≠90°
Common Monoclinic Crystals: Azurite,
Epidote, Gypsum, Moonstone, Muscovite
(Mica), Serpentine
Triclinic System
Triclinic, also known as anorthic, is a crystal
system with the lowest symmetry. In this
system there are no restrictions on angles or
sides.
a ≠b ≠c
α ≠β ≠γ
Common Triclinic Crystals: Feldspar,
Kyanite, Turquoise
Amorphous
No crystal structure. Most of these are either
cooled too quickly to crystallize - such as
obsidian or moldavite, or are organic - such as
amber.
